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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 103 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is √121? =
  2. 2.What is √289? =
  3. 3.What is 69²? =
  4. 4.A square garden has an area of 784 square m. How long is each side (in m)?
  5. 5.What is √7225? =
  6. 6.Which of these is a perfect square? (a) 682 (b) 676 (c) 694
  7. 7.Which of these is a perfect square? (a) 1378 (b) 1369 (c) 1399
  8. 8.What is 24²? =
  9. 9.A square garden has an area of 144 square m. How long is each side (in m)?
  10. 10.How many whole numbers lie between 19² and 20²?
  11. 11.How many whole numbers lie between 41² and 42²?
  12. 12.What is the smallest whole number by which 176 must be divided to get a perfect square?
  13. 13.What is 12²? =
  14. 14.What is √961? =
  15. 15.How many whole numbers lie between 33² and 34²?
  16. 16.Which of these is a perfect square? (a) 439 (b) 404 (c) 400
  17. 17.How many whole numbers lie between 48² and 49²?
  18. 18.What is 89²? =
  19. 19.What is 21²? =
  20. 20.A square garden has an area of 2704 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 362 (b) 361 (c) 378
  22. 22.Which of these is a perfect square? (a) 307 (b) 295 (c) 289
  23. 23.What is √2304? =
  24. 24.What is 17²? =
  25. 25.What is √3481? =
  26. 26.What is √676? =
  27. 27.What is √4761? =
  28. 28.What is 79²? =
  29. 29.What is 48²? =
  30. 30.How many whole numbers lie between 21² and 22²?
  31. 31.What is 19²? =
  32. 32.How many whole numbers lie between 20² and 21²?
  33. 33.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 2601 square m. How long is each side (in m)?
  36. 36.What is 28²? =
  37. 37.Which of these is a perfect square? (a) 591 (b) 576 (c) 619
  38. 38.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
  39. 39.What is 57²? =
  40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 11
  2. 17
  3. 4761
  4. 28
  5. 85
  6. 676
  7. 1369
  8. 576
  9. 12
  10. 38
  11. 82
  12. 11
  13. 144
  14. 31
  15. 66
  16. 400
  17. 96
  18. 7921
  19. 441
  20. 52
  21. 361
  22. 289
  23. 48
  24. 289
  25. 59
  26. 26
  27. 69
  28. 6241
  29. 2304
  30. 42
  31. 361
  32. 40
  33. 10
  34. 81
  35. 51
  36. 784
  37. 576
  38. 13
  39. 3249
  40. 529

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